Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C41 · Schur multiplier (H2) = C2 |
| direct product | D3×C41×D25 |
| unambiguous semidirect product | (D3×C25)⋊(C2×C41) |
| unambiguous semidirect product | (C3×D25)⋊(C2×C41) |
| unambiguous semidirect product | D75⋊(C2×C41) |
| Fitting, Hall | C3×C25×C41 ⋊ C22 |
| derived, Hall | C3×C25 ⋊ C22×C41 |
| Hall | C25×C41 ⋊ C2×D3 |
| Hall | C3×C41 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×D3×C41 |
| Sylow | C3 ⋊ C2×C41×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D3×D25 |
| commutator, cosocle, hypocenter | C3×C25 | C22×C41 |
| Frattini | C5 | D3×D5×C41 |
| Fitting | C3×C25×C41 | C22 |
| socle | C3×C5×C41 | C2×D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C41 | |
60 conjugacy classes of subgroups.
1722 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C41×D25, C3×D3×C41×D25, C3⋊D3×C41×D25, … |
| maximal normal subgroup of | C3×D3×C41×D25 |
| maximal quotient of | D9×C41×D25, C3×D3×C41×D25, C3⋊D3×C41×D25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 37);